Problem

If you use Tomcat to run Java apps such as Atlassian Confluence (the page you're looking at now), JIRA, etc, via HTTPS, you might have noticed that your app will not support any 256 bit ciphers, however it will support 128 and 168 bit ciphers, as well as the lame 40 and 56 bit ciphers. The sslscan tool confirms this, and reports:

Due to import control restrictions for some countries, the Java Cryptography Extension (JCE) policy files shipped with the Java SE Development Kit and the Java SE Runtime Environment allow strong but limited cryptography to be used.

Enable 256 bit ciphers

From the Sun website, download the JCE Unlimited Strength Jurisdiction Policy Files 6 Release Candidate.
Unpack the ZIP file - it will contain two jar files: local_policy.jar and US_export_policy.jar.
On our Ubuntu boxes we use the packages sun-java6-jdk, sun-java6-bin, and sun-java6-jre. The files in question are stored in /usr/lib/jvm/java-6-sun/jre/lib/security. Replace the default jar files with the ones you downloaded, then restart your app. It should now support 256 bit ciphers:

Disable 40 and 56 bit ciphers

By default, also 40 and 56 bit ciphers are supported - you probably want to disable these. To do so you have to explicitly configure the allowed ciphers: take the previous list, include the 256 bit ciphers, leave out the 40 and 56 bit ones, then put the official names (not the OpenSSL equivalent) of the remaining ciphers in your HTTPS config (in my case at the bottom of server.xml). This will look like this:

After restarting your app, you can verify with sslscan that now 256 bit ciphers are supported and preferred, and no 40 and 56 bits ones are available anymore: